Electronic teaching device

ABSTRACT

An electronic teaching device (10) provides several mathematical activities including Place Value, Trade, Target, Solve It, Word Problems, Estimate, Select and Calculator. The Place Value activity enhances the understanding of numbers by pictorially displaying the place values. The Trade activity enhances the understanding of addition and subtraction by allowing the user to trade between the ones&#39; place value and the tens&#39; place value to properly perform a mathematical operation. The Target activity emphasizes logical reasoning and problem solving. The Solve It activity uses the place-value system to develop logical reasoning. 
     The Word Problems activity tests the user&#39;s knowledge of basic mathematical terms and facts. The Estimate activity develops the ability to estimate answers to problems. The Select activity allows the user to recognize basic math operations.

RELATED APPLICATIONS

This application is related to U.S. patent application Ser. No. 560,626, filed Jul. 31, 1990 by Thornton et al., entitled "Electronic Teaching Device," and U.S. patent application Ser. No. 560,656, filed Jul. 31, 1990, by Howard et al., entitled "Electronic Teaching Device", filed concurrently herewith.

TECHNICAL FIELD OF THE DISCLOSURE

This invention relates in general to educational products, and more particularly to an electronic device for teaching mathematics.

BACKGROUND OF THE DISCLOSURE

The advent of consumer electronics has resulted in a number of electronic teaching devices. One field to which the electronic teaching devices have been applied is the study of mathematics. These devices have focused on presenting mathematics through numerical representations, i.e., the digits "0" through "9." The position of these digits in a character string represents the base ten numbering system.

By teaching mathematics through numerical representation, the play patterns are limited to drill and practice activities for children already familiar with the basic concepts of the base ten numbering system. Thus, these electronic teaching devices do not help children understand base ten system, but rather, merely improve their math skills through repetition.

Some devices represent numbers by counting objects. While this method can be practiced by children without knowledge of the base ten numbering system, it does not improve the child's understanding of the base ten numbering system because it does not teach the integral concept of place value.

Therefore, a need has arisen in the industry for an electronic teaching device which graphically presents mathematics associated with the base ten, or other base, numbering system.

SUMMARY OF THE DISCLOSURE

In accordance with the present invention, an electronic learning device is provided which substantially eliminates disadvantages associated with prior art devices.

In the present invention, an electronic teaching device comprises graphical display circuitry for representing the value of a number by presenting objects representative of the respective place values of the number, corresponding to a predetermined base. Numerical display circuitry is associated with the graphical display circuitry and is operable to represent the value of the number by numerical representation.

The present invention provides several technical advantages over the prior art. The user develops a high degree of understanding of the number system through the graphical representation of the numbers.

In a second aspect of the present invention, addition and subtraction may be performed, using the numerical display to present the equation. Objects may be traded between places to graphically complete the operation.

This aspect of the invention provides a greater understanding of the interaction between the number system and the mathematical operations.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which:

FIG. 1 illustrates a perspective view of a preferred embodiment of the present invention;

FIG. 2 illustrates a diagram of a preferred embodiment of the display used with the present invention;

FIG. 3 illustrates a block diagram of the circuitry used in the preferred embodiment;

FIGS. 4a-c illustrate a function of the present invention wherein the user enters a numerical representation of the number based on a graphical representation supplied by the present invention;

FIGS. 5a-c illustrate a function of the present invention wherein the user enters a graphical representation of a number based on numerical representation generated by the present invention;

FIGS. 6a-c illustrate use of a graphical representation of numbers to demonstrate addition;

FIGS. 7a-c illustrate use of the graphical representation of numbers to demonstrate subtraction;

FIGS. 8a-e illustrate the "Target" function of the present invention;

FIGS. 9a-h illustrate the "Solve-it" function of the present invention;

FIGS. 10a-c illustrate the "Estimate" function of the present invention; and

FIGS. 11a-b illustrate the "Select" function of the present invention.

DETAILED DESCRIPTION OF THE DISCLOSURE

The preferred embodiment of the present invention is best understood by referring to FIGS. 1-6 of the drawings, like numerals being used for like and corresponding parts of the various drawings.

FIG. 1 illustrates a front view of the electronic teaching device of the present invention. The electronic teaching device 10 comprises an outer shell 12 including a handle 14, a speaker grill 16, memory port 18, keyboard 20, display 22, and contrast adjustment knob 24. The keyboard 20 is typically a planar keyboard comprising a plurality of switches depicted on a plastic overlay. On/Off switches 26 and 28 allow the user to turn the electronic teaching device 10 on or off, respectively. A first row of keys sets forth the different functions of the electronic device: "Place Value" 30, "Trade" 32, "Target" 34, "Solve It" 36, "Word Problems" 38, "Estimate" 40, "Select" 42, and "Calc" 44. The Place Value function key 30 includes a "ones" place value key 46 and a "tens" place value key 48. The Trade function key 32 includes a "ten to ones" trade key 50 and a "ones to ten" trade key 52. The keyboard additionally comprises an Enter key 54, a Clear/Clear Entry key 56, a calculator keypad 58 including digits "0-9", ".", "=", and the basic mathematical operators "+", "-", "×", and "+". Additionally, up, down, left and right cursor keys 60, 62, 64 and 66 are provided along with a "Repeat" key 68. "Level", "module", and "players" keys 69a-c are also provided.

The display 22 is shown in greater detail in FIG. 2. The display 22 comprises a first row 70 of arrays 70a-d, a second row 72 of arrays 72a-d and a third row 74 of arrays 74a-e. Each of the arrays 70a-d, 72a-d and 74a-e are operable to display a numerical representation of a digit along with letters and symbols. An operation array 76 is operable to display a representation of the four basic mathematical operations. Vertical bar 78 and horizontal bar 80 may be used together to form a divisor symbol or horizontal bar 80 may be used by itself as a result bar. Digits "1"-"9" may be displayed by outputs 82a-i (referred to generally as digits 82). A column of bars 84a-i (referred to generally as bars 84), representing the ten's place value are disposed to the right of digits 82. A column of unit blocks 86a-i (referred to generally as blocks 86) representing the one's place are disposed to the right of bars 84; overflow blocks 88a-i (referred to generally as overflow blocks 88) are provided next to unit blocks 86 for instances when the one's place value exceeds nine blocks because of a mathematical operation. Left and right arrows 90 and 92 are available to display a carry or borrow situation, respectively.

FIG. 3 illustrates a block diagram of the circuitry used in the preferred embodiment of the present invention. The circuit 94 includes a microprocessor 96 having a program memory 98. The microprocessor is coupled to a speech ROM 100 and an optional speech ROM 102 which hold the speech data. Further, the microprocessor is connected to the keyboard 20 through a 3-to-8 decoder 104 and through a parallel-to-serial shift register 106. The microprocessor outputs data to the display 22 through an LCD driver 108. Audio output is provided through speaker 110. In the preferred embodiment, the microprocessor 96 comprises a speech synthesizing microprocessor such as the Texas Instruments Inc. 50C10, which has an internal 8k memory. The speech ROMs 100 and 102 may comprise a TI60C18, 32k ROM, or equivalent. The parallel-to-serial shift register may comprise a TI74HC165 and the 3-to-8 decoder may comprise a TI74HC138.

In operation, the microprocessor executes a program stored in the internal memory 98 to provide various functions as described below. The speech ROM 100 stores the speech data for synthesized speech output. The additional speech ROM 102 may be plugged into the memory port 18 to provide additional speech capabilities. The 3-to-8 decoder is used to decode a 3-bit address such that one keyboard row may be scanned at a time to determine whether the user is pressing a key. This implementation reduces the number of lines necessary to scan the keyboard for input. The output of keyboard is translated through the parallel-to-serial shift register 106 to provide output to the microprocessor.

Referring to FIGS. 1-3, the overall operation of the electronic teaching device 10 is described. By pressing the On key 26, the computer uses speech synthesis to request the user to press one of the function keys 30-44. The basic concepts associated with each key are as follows:

    ______________________________________                                         FUNCTION     CONCEPTS                                                          ______________________________________                                         Place Value  Teaches the place value system in                                              representing one- and two-digit                                                numbers.                                                          Trade        Reenforces understanding of the Place                                          Value system.                                                     Target       Emphasizes logical reasoning and                                               problem-solving.                                                  Solve It     Uses the Place Value system to                                                 develop logical reasoning.                                        Word Problems                                                                               Tests the user's knowledge of basic                                            mathematical terms and facts.                                     Estimate     Develops the ability to estimate the                                           answers to problems.                                              Select       Helps the user recognize basic math                                            operations.                                                       Calculator   Provides the user the opportunity to                                           make up and solve his or her own math                                          problems.                                                         ______________________________________                                    

To select an activity, the corresponding function key 30-44 is pressed. The teaching device 10 repeats the name of the activity and the level of play and prompts the first user if the teaching device 10 is in a 2-player mode. The level of difficulty can be adjusted by pressing the Level key 69a. The one- or two-player mode may be toggled by pressing the Player key 69c. If the optional speech ROM 102 is plugged into the port 18, the user may toggle between the two ROMs by pressing the module button 69b.

Referring to FIGS. 1, 2, 4a-c and 5a-c, the Place Value function is described. To select the Place Value activity, the user presses the Place Value function key 30. Optionally, the user may use the Level and Player keys 69a and 69c to change the level of challenge or the number of players. For purposes of clarity, the Place Value activity will be discussed herein as if played by a single player.

After pressing the Place Value key 30 (i level 2), the electronic teaching device asks the user, "What number is this?" and displays a number of unit blocks 86 and bars 84. Each block 86 represents a "one" and each bar 84 represents a "ten." To illustrate the relative magnitude of the bars 84 and blocks 86, the bars have approximately ten times the area as blocks 86. A flashing box 74e (flashing denoted in the FIGURES by a dashed outline) in the one's place (on the bottom line of the display) prompts the user to enter the Number key in the calculator keypad 58 which represents the correct number of ones. Simultaneously, the unit blocks 86 are flashing. After the user has entered his or her answer for the number of unit blocks 86, the electronic teaching device 10 repeats the number of ones which has been entered. The flashing box then moves to the tens place, as shown in FIG. 4b. In FIG. 4b, the user has correctly entered the number "4" to indicate the number of unit blocks 86 displayed.

Once the number representing the unit blocks 86 has been entered, the bars 84 flash and a flashing box 74d prompts the user to enter the number of bars. Once again, the user uses the keypad 58 to enter the number representing the tens' place. As shown in FIG. 4c, the user has correctly entered "3." After pressing the Enter key, the teaching device 10 will provide a response such as "That's great" to indicate a correct answer or will respond "Sorry, try again" for an incorrect answer.

The second level of the Place Value activity is illustrated in FIGS. 5a-c. In this activity, the teaching device 10 asks "How many blocks?" and shows a number in the display, illustrated in FIG. 5a as the number "23". The user enters the number of unit blocks 86 by pressing the ones Place Value key 46 the correct number of times. As shown in FIG. 5b, the user has pressed the ones Place Value key three times. Similarly, as shown in FIG. 5c, the user presses the tens Place Value key 48 twice to represent the tens digit shown in the display block 74d. After entering the correct number of tens bars and ones blocks, the user presses the Enter key 54 and the teaching device responds positively or negatively, depending upon the correctness of the answer.

The third level of the Place Value activity asks questions from both Level 1 and Level 2.

The Trade activity is illustrated in connection with FIGS. 6a-c and 7a-c. The Trade activity has three levels of challenge and can be played by one or two players. The object is to regroup the ones-blocks 86 and 88 and tens-bars 84 to reflect the answer. The user is permitted two tries to answer correctly.

The first level of the Trade activity teaches addition and the second level of the Trade activity teaches subtraction. The third level is combination of addition and subtraction.

FIGS. 6a-c illustrate the first level of the Trade activity. After pressing the Trade function key 32, the teaching device 10 asks the user to "Make the Trade," and an addition problem appears in the display, such as the one illustrated in FIG. 6a. In this FIGURE, the addition problem of "28+37" is displayed along with the number of blocks corresponding to addition of each place value. Hence, fifteen unit and overflow blocks 86 and 88 are shown along with five bars 84. The group of unit and overflow blocks 86 and 88 and bars 84 that represent the number on the second line of the display, i.e., seven unit blocks 88 and three bars 84, flash. The non-flashing blocks 86 and bars 84 represent the number on the first line of the display. The arrow 90 is flashing to point in the direction which the trade should be made. To trade ones for a ten, the ones to ten Trade key 52 is pressed. To trade a ten for ones, the ten to ones Trade key 50 is pressed. When a Trade key 50 or 52 is pressed, the blocks in the display change to reflect the trade.

After the trade is made, as shown in FIG. 6b, the blocks stop flashing. These blocks represent the answer. The user is then prompted by the flashing boxes 74d-e to enter the number of ones and then the number of tens by using the keypad 58. As shown in FIG. 6c, the user has correctly entered "65" as the answer. The teaching device 10 then indicates the correctness of the answer by a positive or a negative response.

The second level of the Trade activity is illustrated in connection with FIGS. 7a-c. Once again, an equation, shown in FIG. 7a as 98-69, is displayed along with a number of bars and blocks which represent the minuend. The number ones in the place of the minuend will be less than the number in the ones' place of the subtrahend. Hence, a borrow must be performed to trade a ten for ones, the ten to ones Trade key 50 is pressed and ten unit blocks 86 and 88 are added to the display and one bar 84 is removed. The number of bars 84 representing the value of the tens' place of the subtrahend flash along with the number of blocks 86 and 88 representing the value of the ones' place of the subtrahend. Hence, the non-flashing bars 84 and blocks 86 represent the answer, as shown in FIG. 7b. In FIG. 7c, the user enters the answer using the keypad 58 and the Enter key 54. Once again, the teaching device responds to the correctness of the answer.

A third level of the Trade activity is a combination of addition and subtraction problems.

FIGS. 8a-e illustrate the Target activity. In this activity, one player can play against the teaching device 10, or two players can play against each other. The object is to be the first to arrive at a target number selected by the teaching device 10.

After selecting the Target activity by pressing the Target function button 34, the teaching device responds by choosing a target number and three other numbers players can use to reach the target. For example, in the FIG. 8a, the teaching device 10 has chosen a target of "23" and provided numbers "1, 2 and 7" (as displayed by digits 82) for the players to use to reach the target. Initially, the accumulated sum is set to zero. In FIG. 8b, the first player chooses a "7". In FIG. 8c, the second player chooses a "7" as well, rendering an accumulated sum of "14." In FIG. 8d, the first player chooses a "7" for an accumulated sum of "21." In FIG. 8e, the second player chooses a "2" to hit the target value of "23." The numbers are entered by the users on the keypad 58. If the target is exceeded by a player, the opponent player wins. If the activity is in the one player mode, the teaching device 10 selects numbers for the second player. After the target is reached or exceeded, the teaching device announces the winner.

This activity challenges the user to think ahead to determine the possible combinations of numbers which may be used to reach the target.

FIGS. 9a-h illustrate the Solve It activity. This activity is three levels of challenge and can be played by one or two players. The object is to arrange the displayed numbers to get the largest or smallest sum, difference, quotient or product. Generally, it is requested that the result be positive.

In FIGS. 9a-b, the teaching device has selected number "1, 2 and 3" (as displayed by digits 82) to be arranged in an addition problem by the user to derive the largest sum. The user positions the available numbers using the keypad 58 and the arrow keys 60-66 to arrange the numbers as shown in FIG. 9b. The number of digits appearing in the problem depends upon the level of play.

Once the numbers are entered, the Enter key 54 is pressed. The teaching device 10 responds positively or negatively, depending upon the correctness of the answer. After two incorrect tries, the teaching device 10 displays the equation and answer and then repeats them orally.

FIGS. 9c and d illustrate the Solve It activity using division. In this case, a division sign is produced by vertical line 78 and horizontal line 80 by the teaching device and five underlines are provided by arrays 74a-e to indicate placement of the available numbers, illustrated in FIG. 9c as "3, 5, 6, 7 and 8." In this example, the teaching device has requested that the largest positive quotient be determined. In FIG. 9d, the user has properly arranged the numbers as "8765" divided by "3." After the user presses the Enter key, the quotient of "2921" with a remainder of "2" is displayed by the teaching device 10 and is orally repeated.

In FIGS. 9e and f, a multiplication problem is illustrated for the Solve It activity. In this example, the teaching device 10 has chosen the numbers "2, 3, 7, 8 and 9" and a multiplication sign is provided. In this example, the teaching device requests that the user find the smallest positive solution. In FIG. 9f, the user has properly arranged the numbers as "389" times "27." After pressing the Enter key, the teaching device 10 displays the correct answer, "10503."

FIGS. 9g and h illustrate a subtraction problem using the Solve It activity. In this case, the teaching device 10 has chosen the numbers "1, 2, 4, 6 and 8" and requested the largest positive solution. In FIG. 9h, the user has properly arranged the numbers as "864" minus "12." After pressing the Enter key, the teaching device displays and repeats the answer "852."

The Word Problem activity has three levels of challenge. It can be played by one or two players. The object is to listen to the word problems and type in the numerical answer. The Word Problem activity is selected by pressing the Word Problem function key 38. The teaching device 10 states a question such as "I am a prime number between 70 and 80. The sum of my digits is 10. What am I?". The correct answer is "73", which may be entered by the user using the keypad 58. Another question might be "What is next? 5,7,11,19 . . . ". The correct answer is "35" (the difference between sequential numbers in the sequence doubles with each additional number). During the Word Problem activity, the calculator may be used to determine the answers to the problems. After a round of five problems, the score is announced. Additional word problems may be provided by the optional ROM 102.

The Estimate activity has three levels of challenge. The object is to estimate, as closely as possible, the answer to a problem in as little time as possible.

FIGS. 10a-c illustrate a multiplication problem. In FIG. 10a, the teaching device 10 provides the equation "333×69=₋₋ 000." Zeros that appear on the third line of the display represent digits which the user does not have to estimate. The user keys in his estimate using the keypad 58. As shown in FIG. 10b, the user has estimated the answer to equal "21,000" by pressing "21" on the keypad 58 and pressing the Enter key 54. In FIG. 10c, the teaching device 10 produces a score based on how fast and close the answer is to the correct answer. As illustrated, the user has answered the question within four seconds with an accuracy of ±10% for a score of "99". The Estimate activity also provides subtraction, addition and division problems. For example, the teaching device 10 may provide an equation of "366+962=₋₋ 00." An example of a division equation would be "5568÷7=₋₋ 00." An example of subtraction equation would be "666-105=₋₋ 0."

FIGS. 11a-b illustrate the Select activity. This activity has three levels of challenge and can be played by one or two players. The object is to select the correct operation (+, -, ×, or ÷ sign) for a problem that is displayed with its answer. When this activity is selected by pressing the Select function key 42, the teaching device 10 asks the user to "choose the operation" and displays a problem with the operators flashing one after another. As shown in FIG. 11a, the equation "231₋₋ 46=185" is displayed. The user chooses an operation key (-, +, × or ÷ sign) from the keypad 58 and presses the Enter key 54, or presses the Enter key 54 as the particular operator is displayed. In the example of FIG. 11a, the minus sign is the correct answer. After each player completes a round of five problems, the score for each player is announced. This scoring feature is also used for the Place Value, Trade, Solve It, and Word Problem functions.

The Calculator activity is selected by pressing the Calculator function key 44. In this mode of operation, the keypad 58 acts as a four-function calculator. The user may select a problem such as "89×56" and determine the answer without the aid of the teaching device 10. After the answer is determined, the equal sign may be pressed to compare the user's answer with the correct answer.

The teaching device of the present invention provides several advantages over the prior art. The Place Value and Trade activities provide a pictorial representation of both numbers and of the addition and subtraction operations, enhancing the user's understanding of the number system. Further, the Target, Solve It, Word Problems, Estimate and Select activities challenge the user into approaching mathematical operations from different perspectives to enhance his or her learning. Further, activities may be played as a contest between two players, increasing the challenge to learn. The different levels of difficulty allow the teaching device to be used over a long time period.

Although the present invention has been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims. 

What is claimed is:
 1. An electronic apparatus for teaching mathematics comprising:memory means having digital data stored therein including numbers control digital data representative of numbers and graphics control digital data for providing selective graphical representation of numbers from which a plurality of mathematical problems may be derived for presentation to a user requiring the user to demonstrate a knowledge of the place values of numbers according to a predetermined base number; means operably associated with said memory means for selecting one of numbers control digital data and graphics control digital data as stored in said memory means to derive a particular mathematical problem based thereon; presentation means operably associated with said selection means and including display means for visually presenting one of numbers and graphics from the selected said one of numbers control digital data and graphics control digital data providing the particular mathematical problem; user input means for receiving inputs from the user indicative of an effort leading to a proposed solution of the mathematical problem; comparator means coupled to said selection means and to said user input means for determining the appropriateness of the inputs received by said user input means from the suer with respect to a solution of the mathematical problem; and means coupled to said comparator means for producing an indication of the accuracy of the input from the user as received by said user input means in relation to the correct solution to the corresponding mathematical problem; said display means including:a plurality of number display arrays arranged in at least one row, each of said number display arrays being operable to display a representation of an individual digit from "0" to "9", and a plurality of graphical display positions arranged in proximity to said plurality of number display arrays and including first and second distinct series of graphical display units representing respective place values of a number corresponding to a predetermined base number, said first series of graphical display units comprising a plurality of graphical display units representing the one's place value, and said second series of graphical display units comprising a plurality of graphical display units equal in number to the plurality of graphical display units of said first series and representing the predetermined base number's place value; one of said respective number display arrays and said graphical display units of said first and second distinct series of graphical display units being selectively activated in response to the selection of one of said numbers control digital data and said graphics control digital data by said selection means so as to visually display the mathematical problem in the form of one of a number and graphics to a user for solution.
 2. An electronic apparatus for teaching mathematics as set forth in claim 1, wherein said one of said numbers control digital data and said graphics control digital data as selected by said selection means comprises number control digital data;said display means of said presentation means visually presenting a number form the selected numbers control digital data in said number display arrays from providing the particular mathematical problem; and said user input means receiving inputs from the user representative of individual graphical display units for corresponding to the one's place value and the base number's place value of the visually displayed number as a proposed solution of the mathematical problem.
 3. An electronic apparatus for teaching mathematics as set forth in claim 1, wherein said one of said numbers control digital data and said graphics control digital data as selected by said selection means comprises graphics control digital data;said display means of said presentation means visually presenting graphics from the selected graphics control digital data for providing the particular mathematical problem by selectively activating respective graphical display units of said first and second distinct series of graphical display units in response to the selection of graphics control digital data by said selection means so as to visually display the mathematical problem in graphics form to a user for solution; and said user input means receiving inputs from the user indicative of numbers representative of the respective place values of a number corresponding to the number of selectively activated graphical display units of said first and second distinct series of graphical display units as a proposed solution of the mathematical problem.
 4. An electronic apparatus for teaching mathematics as set forth in claim 1, wherein said first and second distinct series of graphical display units representing respective place values of a number corresponding to a predetermined base number are proportional in size to their respective place values.
 5. An electronic apparatus for teaching mathematics as set forth in claim 4, wherein the predetermined base number is 10;said first series of graphical display units being representative of the one's place value, and said second series of graphical display units being representative of the ten's place value; and the size of the graphical display units included in said second series being ten times greater in area than the size of the graphical display units included in said first series.
 6. An electronic apparatus for teaching mathematics as set forth in claim 1, wherein said first series of graphical display units comprise a column of display unit block laterally spaced from said at least one row of number display arrays; andsaid second series of graphical display units comprises a column of elongated display bars interposed between said at least one row of number display arrays and said column of display unit blocks in laterally spaced relationship with respect thereto.
 7. An electronic apparatus for teaching mathematics as set forth in claim 6, wherein the size of each of said elongated display bars is ten times greater in area than the size of corresponding display unit blocks in the column thereof.
 8. An electronic apparatus for teaching mathematics as set forth in claim 6, further including a column of display overflow blocks laterally spaced from said column of display unit blocks and operable to represent overflow when the one's place values exceeds the number of display unit blocks included in the column thereof.
 9. An electronic apparatus for teaching mathematics as set forth in claim 1, wherein said presentation means further includes speech synthesizer means coupled to said selection means and to said memory mean for generating analog signals representative of human speech, and audio means coupled to said speech synthesizer means for converting said analog signals into audible human speech for audibly announcing the nature of the selected mathematical problem to the user as a request for the solution to the mathematical problem.
 10. An electronic apparatus for teaching mathematics as set forth in claim 9, wherein said accuracy indicating means comprises means for causing said speech synthesizer means and said audio means coupled thereto to present an audible announcement in a human language of the results of the comparison between the inputs form the user as received by said user input means and the correct solution to the mathematical problem.
 11. An electronic apparatus for teaching mathematics comprising:memory means having digital data stored therein including numbers control digital data representative of numbers and graphics control digital data for providing selective graphical representation of numbers and a mathematical operator including one of additional and subtraction from which a plurality of mathematical problems may be derived for presentation to a user requiring the user to demonstrate a knowledge of the place values of numbers according to a predetermined base number; means operably associated with said memory means for selecting a mathematical operator, a plurality of numbers as a set corresponding to numbers control digital data, and a plurality of graphical units corresponding to graphics control digital data as stored in said memory means, said selected plurality of graphical units being related to said selected set of numbers to derive a particular mathematical problem involving the selected mathematical operator; presentation means operably associated with said selection means and including display means for visually presenting the mathematical operator, the selected set of numbers, and the selected plurality of graphical units, one portion of the selected plurality of graphical units appearing visually different from the other portion of the selected plurality of graphical units; user input means for receiving inputs from the user indicative of an effort leading to a proposed solution of the mathematical problem; comparator means coupled to said selection means and to said user input means for determining the appropriateness of the inputs received by said user input means form the user with respect to a solution of the mathematical problem; and means coupled to said comparator means for producing an indication of the accuracy of the input from the user as received by said user input means in relation to the correct solution to the corresponding mathematical problem; said display means including:a plurality of number display arrays arranged in a plurality of rows, each of said number display arrays being operable to display a representation of an individual digit from "0" to "9", at least one mathematical operation display array operable to display a symbolic representation of one of the arithmetical operations of additional and subtraction as a mathematical operator, a horizontally extending result bar disposed between at least two rows of number display arrays and a further row of number display arrays, `a plurality of graphical display positions arranged in proximity to said plurality of number display arrays and including first and second distinct series of graphical display units representing respective place values of a number corresponding to a predetermined base number, said first series of graphical display units comprising a plurality of graphical display units representing the one's place value, and said second series of graphical display units comprising a plurality of graphical display units equal in number of the plurality of graphical display units of said first series and representing the predetermined base number's place value, and a third series of graphical display units representing overflow graphical display units when the one's lace value exceeds the number of graphical display units of said first series; the selected set of numbers and the mathematical operator being respectively visually displayed in said plurality of rows of number display arrays and said at last one mathematical operation display array, and the respective graphical display units of said first and second distinct series of graphical display units and said overflow graphical display units of said third series of graphical display units being selectively activated in response to the selection of graphics control digital data by said selection means in visually displaying the mathematical problem to a user for solution; and one of said numbers included in said set of numbers correspond to said one portion of the selected plurality of graphical units and the other number of said set of numbers corresponding to said other portion of the selected plurality of graphical units in visually displaying the mathematical problem to the user for solution.
 12. An electronic apparatus for teaching mathematics as set forth in claim 11, wherein said user input means includes first and second trade modes, said first trade mode being representative of the trading of one's place values for the base number's base value, and the second trade mode being representative of trading a base number's place value for one's place values; andsaid selected plurality of graphical units being modified in response to the selective actuation of one of said first and second trade modes by the user.
 13. An electronic apparatus for teaching mathematics as set forth in claim 12, wherein the mathematical operator is addition.
 14. An electronic apparatus for teaching mathematics as set forth in claim 12, wherein the mathematical operator is subtraction.
 15. An electronic apparatus for teaching mathematics as set forth in claim 11, wherein said first series of graphical display units comprises a column of display unit blocks laterally spaced from said plurality of number display arrays;said second series of graphical display units comprises a column of elongated display bars interposed between said plurality of number display arrays and said column of display unit blocks and laterally spaced therefrom; and said plurality of overflow graphical display units comprises a column of display overflow blocks laterally spaced form said column of display unit blocks and representing overflow when the one's place value exceeds the number of display unit blocks included in the column of display unit blocks.
 16. An electronic apparatus for teaching mathematics as set forth in claim 11, wherein the predetermined base number is 10;said second series of graphical display units representing the ten's place value, and said first series of graphical display units representing the one's place value; and the size of each of said graphical display units included in said second series being ten times greater in area than the size of said graphical display units included in said first series.
 17. An electronic apparatus for teaching mathematics as set forth in claim 11, wherein said presentation means further includes speech synthesizer means coupled to said selection means and to said memory means for generating analog signals representative of human speech, and audio means coupled to said speech synthesizer means for converting said analog signals into audible human speech for audibly announcing the nature of the selected mathematical problem to the user as a request for the solution to the mathematical problem.
 18. An electronic apparatus for teaching mathematics as set forth in claim 17, wherein said accuracy indicating means comprises means for causing said speech synthesizer means and said audio means coupled thereto to present an audible announcement in a human language of the results of the comparison between the inputs from the user as received by said user input means and the correct solution to the mathematical problem.
 19. An electronic apparatus for teaching mathematics as set forth in claim 11, wherein said one portion of the selected plurality of graphical units exhibits a pulsating visibility in contrast to the other portion of the selected plurality of graphical units in visually displaying the particular mathematical problem to the user for solution.
 20. An electronic apparatus for teaching mathematics as set forth in claim 19, wherein the mathematical operator is addition when said one portion of the selected plurality of graphical units is initially displayed in a visual pulsating manner.
 21. An electronic apparatus for teaching mathematics as set forth in claim 19, wherein said one portion of the selected plurality of graphical units appears as a pulsating visual display after the initial presentation of the mathematical problem in visual form to the user for solution.
 22. An electronic apparatus for teaching mathematics as set forth in claim 21, wherein the mathematical operator is subtraction when said one portion of the selected plurality of graphical units appears as a pulsating visual display after the initial presentation of the mathematical problem in visual form to the user for solution. 